Sequences at Baseband

Communication waveforms in which the received pulses, after filtering, are not Nyquist pulses cannot be optimally demodulated one symbol at a time. The pulses will overlap and the samples will interact. This interaction is called intersymbol interference . Rather than use a Nyquist pulse to prevent intersymbol interference, one may prefer to allow intersymbol interference to occur and to compensate for it in the demodulation process. In this chapter, we shall study ways to demodulate in the presence of intersymbol interference, ways to remove intersymbol interference, and in Chapter 9, ways to precode so that the intersymbol interference seems to disappear. We will start out in this chapter thinking of the interdependence in a sequence of symbols as undesirable, but once we have developed good methods for demodulating sequences with intersymbol interference, we will be comfortable in Chapter 9 with intentionally introducing some kinds of controlled symbol interdependence in order to improve performance. The function of modifying a channel response to obtain a required pulse shape is known as equalization . If the channel is not predictable, or changes slowly with time, then the equalization may be designed to slowly adjust itself by observing its own channel output; in this case, it is called adaptive equalization . This chapter studies such interacting symbol sequences, both unintentional and intentional. It begins with the study of intersymbol interference and ends with the subject of adaptive equalization.